Problem: Simplify the following expression: $ k = -1 - \dfrac{7r + 1}{6r} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{6r}{6r}$ $ \dfrac{-1}{1} \times \dfrac{6r}{6r} = \dfrac{-6r}{6r} $ Therefore $ k = \dfrac{-6r}{6r} - \dfrac{7r + 1}{6r} $ Now the expressions have the same denominator we can simply subtract the numerators: $k = \dfrac{-6r - (7r + 1) }{6r} $ Distribute the negative sign: $k = \dfrac{-6r - 7r - 1}{6r}$ $k = \dfrac{-13r - 1}{6r}$